A wide variety of different types of storage systems are known. For example, some storage systems are configured to include multiple storage tiers, with different ones of the tiers providing different levels of performance or other characteristics. In such storage systems, data may be moved from one tier to another within a given storage system based on access frequency of the data or other factors. These and other types of tiered or non-tiered storage systems may be shared by multiple host devices of a compute cluster. However, problems can arise in such arrangements in that some storage systems are configured to differentiate performance only on the basis of a storage device or a group of storage devices. A user desiring different levels of performance for different processes of an application running on a host device may therefore have to designate separate storage devices or groups of storage devices within the storage system for handling input-output operations of each of the different processes of the application. Another possible approach is for the host device to provide out-of-band hints indicating particular storage device extents that are used by the different processes, but such an approach is unduly complex and can adversely impact input-output performance. For example, the storage device extents used by the different processes can dynamically change over time and therefore must be carefully managed on both the host devices and the storage array.